Extrude a mesh by Region using Python script
This should do the trick, and no need to create a bmesh object to extrude all your mesh's faces:

import bpy

# Go to edit mode, face selection mode and select all faces
bpy.ops.object.mode_set( mode   = 'EDIT'   )
bpy.ops.mesh.select_mode( type  = 'FACE'   )
bpy.ops.mesh.select_all( action = 'SELECT' )

bpy.ops.mesh.extrude_region_move(
    TRANSFORM_OT_translate={"value":(0, 0, 3)}
)

bpy.ops.object.mode_set( mode = 'OBJECT' )


Often you can find hints about how to call operators from the info panel, and of course the tooltip. In this case they give contradictory hints but both can get be beneficial: